Subgroups — C₂×D₇₇₅₅ #44526697

Order 31020.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₇₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₅₈₅	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₅₅₁	—	5	1	no	maximal, Hall
6	D₂₅₈₅	—	3	2	no	—
7	C₂×C₅×C₁₁×C₄₇	D₃	1	1	yes	characteristic, complemented
8	D₁₅₅₁	—	5	2	no	—
9	C₂×C₃×C₁₁×C₄₇	D₅	1	1	yes	characteristic, complemented
10	C₂×D₇₀₅	—	11	1	no	maximal, Hall
11	C₅×C₁₁×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×D₅₁₇	—	15	1	no	Hall
13	C₃×C₁₁×C₄₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₄₇	D₁₁	1	1	yes	characteristic, complemented
15	D₇₀₅	—	11	2	no	—
16	C₂×C₁₁×C₄₇	D₁₅	1	1	yes	characteristic, complemented
17	D₅₁₇	—	15	2	no	—
18	C₂×D₂₃₅	—	33	1	no	Hall
19	C₃×C₅×C₄₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₆₅	—	47	1	no	maximal, Hall
21	C₂×D₁₄₁	—	55	1	no	Hall
22	C₁₁×C₄₇	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₄₇	D₃₃	1	1	yes	characteristic, complemented
24	D₂₃₅	—	33	2	no	—
25	C₂×C₃×C₅×C₁₁	D₄₇	1	1	yes	characteristic, complemented
26	D₁₆₅	—	47	2	no	—
27	C₂×C₃×C₄₇	D₅₅	1	1	yes	characteristic, complemented
28	D₁₄₁	—	55	2	no	—
29	C₅×C₄₇	C₂×D₃₃	1	1	yes	characteristic, complemented, Hall
30	C₂×D₅₅	—	141	1	no	Hall
31	C₂×D₄₇	—	165	1	no	Hall
32	C₃×C₅×C₁₁	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
33	C₃×C₄₇	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃₃	—	235	1	no	Hall
35	C₂×C₅×C₁₁	D₁₄₁	1	1	yes	characteristic, complemented
36	D₅₅	—	141	2	no	—
37	C₂×C₄₇	D₁₆₅	1	1	yes	characteristic, complemented
38	D₄₇	—	165	2	no	—
39	C₂×C₃×C₁₁	D₂₃₅	1	1	yes	characteristic, complemented
40	D₃₃	—	235	2	no	—
41	C₂×D₁₅	—	517	1	no	Hall
42	C₅×C₁₁	C₂×D₁₄₁	1	1	yes	characteristic, complemented, Hall
43	C₄₇	C₂×D₁₆₅	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₁₁	—	705	1	no	Hall
45	C₃×C₁₁	C₂×D₂₃₅	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₅	D₅₁₇	1	1	yes	characteristic, complemented
47	D₁₅	—	517	2	no	—
48	C₂×C₁₁	D₇₀₅	1	1	yes	characteristic, complemented
49	D₁₁	—	705	2	no	—
50	C₂×D₅	—	1551	1	no	Hall
51	C₃×C₅	C₂×D₅₁₇	1	1	yes	characteristic, complemented, Hall
52	C₂×D₃	—	2585	1	no	Hall
53	C₁₁	C₂×D₇₀₅	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	D₁₅₅₁	1	1	yes	characteristic, complemented
55	D₅	—	1551	2	no	—
56	C₂×C₃	D₂₅₈₅	1	1	yes	characteristic, complemented
57	D₃	—	2585	2	no	—
58	C₅	C₂×D₁₅₅₁	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	7755	1	no	Sylow
60	C₃	C₂×D₂₅₈₅	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	7755	2	no	—
62	C₂	D₇₇₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇₇₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₁×C₄₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₄₇	C₂
LCS	G ▷ C₃×C₅×C₁₁×C₄₇
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₇₇₅₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₄₇	C₂	semidirect
4. C₃×C₅×C₁₁×C₄₇	C₂²	semidirect
7. C₂×C₅×C₁₁×C₄₇	D₃	semidirect
9. C₂×C₃×C₁₁×C₄₇	D₅	semidirect
11. C₅×C₁₁×C₄₇	C₂×D₃	semidirect
13. C₃×C₁₁×C₄₇	C₂×D₅	semidirect
14. C₂×C₃×C₅×C₄₇	D₁₁	semidirect
16. C₂×C₁₁×C₄₇	D₁₅	semidirect
19. C₃×C₅×C₄₇	C₂×D₁₁	semidirect
22. C₁₁×C₄₇	C₂×D₁₅	semidirect
23. C₂×C₅×C₄₇	D₃₃	semidirect
25. C₂×C₃×C₅×C₁₁	D₄₇	semidirect
27. C₂×C₃×C₄₇	D₅₅	semidirect
29. C₅×C₄₇	C₂×D₃₃	semidirect
32. C₃×C₅×C₁₁	C₂×D₄₇	semidirect
33. C₃×C₄₇	C₂×D₅₅	semidirect
35. C₂×C₅×C₁₁	D₁₄₁	semidirect
37. C₂×C₄₇	D₁₆₅	semidirect
39. C₂×C₃×C₁₁	D₂₃₅	semidirect
42. C₅×C₁₁	C₂×D₁₄₁	semidirect
43. C₄₇	C₂×D₁₆₅	semidirect
45. C₃×C₁₁	C₂×D₂₃₅	semidirect
46. C₂×C₃×C₅	D₅₁₇	semidirect
48. C₂×C₁₁	D₇₀₅	semidirect
51. C₃×C₅	C₂×D₅₁₇	semidirect
53. C₁₁	C₂×D₇₀₅	semidirect
54. C₂×C₅	D₁₅₅₁	semidirect
56. C₂×C₃	D₂₅₈₅	semidirect
58. C₅	C₂×D₁₅₅₁	semidirect
60. C₃	C₂×D₂₅₈₅	semidirect
62. C₂	D₇₇₅₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₇₇₅₅	2
C₂×C₃×C₅×C₁₁×C₄₇	2
C₂×D₂₅₈₅	3
C₂×D₁₅₅₁	5
C₂×D₇₀₅	11
C₂×D₁₆₅	47

Subgroups — C2×D7755 #44526697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇₇₅₅ #44526697